Fig. 1 Method marginalized detrending. Comparison of five different detrending methods on two different Kepler data products (SAP and PDC). The top curve shows the Kepler reduction used in (12), and the bottom curve shows the method marginalized product used in this work. The three panels show the three transits observed by Kepler.
Fig. 2 Hook corrections. (Top) The optimal aperture photometry of our target (left) and the best comparison star (right), where the hooks and visit-long trends are clearly present. Points are colored by their exposure number within each HST orbit (triangles represent outliers). (Middle) A hook correction using the common exponential ramp model on both stars. (Bottom) The result from an alternative and novel hook correction approach introduced in this work. The intra-orbit root mean square (RMS) value is quoted for the hook-corrected light curves.
Fig. 3 HST detrending. The HST observations with three proposed trends fit to the data (left) and with the trends removed (right). Bottom-right numbers in each row give the Bayes factor between a planet plus moon model (model M) and a planet plus moon model where the moon radius equals zero (model Z), which tracks the significance of the moon-like dip in isolation.
Fig. 4 Moon solutions. The three transits in Kepler (top) and the October 2017 transit observed with HST (bottom) for the three trend model solutions. The three colored lines show the corresponding trend model solutions for model M, our favored transit model. The shape of the HST transit differs from that of the Kepler transits owing to limb darkening differences between the bandpasses.
- Table 1 Model performance.
Bayesian evidences (Z) and maximum likelihoods (
) from our combined fits using Kepler and new HST data. Kepler plus HST fits. The subscripts are P for the planet model, T for the planetary TTV model, Z for the zero-radius moon model, and M for the moon model. The three columns are for each trend model attempted.Linear Quadratic Exponential 6302.79 ± 0.11 6306.68 ± 0.11 6308.41 ± 0.11 6304.86 ± 0.11 6308.81 ± 0.12 6310.71 ± 0.11 6306.84 ± 0.11 6311.12 ± 0.12 6310.82 ± 0.12 6315.73 ± 0.12 6312.92 ± 0.12 6314.01 ± 0.12 1.00 ± 0.22* 25.88 ± 0.32 12.47 ± 0.33 11.19 ± 0.32 21.72 ± 0.33 8.21 ± 0.34 17.81 ± 0.33 17.77 ± 0.33 3.61 ± 0.33 6.38 ± 0.34 18.66* 54.93 41.04 41.57 35.69 23.97 23.97 33.68 19.59 19.22 *Values derived using the Kepler data in isolation.
- Table 2 System parameters.
Median and ±34.1% quantile range of the a posteriori model parameters from model M, where each column defined a different visit-long trend model. The top panel gives the credible intervals for the actual parameters used in the fit, and the lower panel gives a selection of relevant derived parameters conditioned upon our revised stellar parameters. The quoted inclination of the satellite is the inclination modulo 90°.
Parameter Linear Quadratic Exponential Photodynamics only RP,Kep/R⋆ RP,HST/RP,Kep ρ⋆,LC [g cm−3] b PP [days] τ0 [BJDUTC] q1,Kep q2,Kep q1,HST q2,HST PS [days] aSP/RP φS [°] iS [°] ΩS [°] (MS/MP) (RS/RP) Δa0 [ppm] + Stellar properties R⋆ [R⊙] M⋆ [M⊙] ρ⋆,iso [kg m−3] RP [R⊕] log10(MP/M⊕) aP [AU] RS [R⊕] log10(MS/M⊕) Seff [S⊕] + forecaster log10(MP/M⊕) log10(MS/M⊕) MP [MJ] [1.2, 12.5] [0.2, 9.0] [0.6, 10.5] MS [M⊕] [4.4, 68] [1.0, 140] [2.6, 76] K [m/s] [35, 380] [6, 280] [18, 320]
Supplementary Materials
Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/10/eaav1784/DC1
Supplementary Materials and Methods
Fig. S1. The “Phantom” star.
Fig. S2. Kepler detrending.
Fig. S3. Kepler detrending comparison.
Fig. S4. HST image rotation.
Fig. S5. HST hook model comparison.
Fig. S6. HST centroids.
Fig. S7. Spectral analysis.
Fig. S8. Transmission spectrum.
Fig. S9. Wavelength solution.
Fig. S10. Wavelength-dependent pixel sensitivity.
Fig. S11. Modeling the uncataloged source contamination.
Fig. S12. Transit timing variations.
Fig. S13. Residual analysis.
Fig. S14. Chromatic test.
Fig. S15. Mass constraints.
Fig. S16. Model posteriors.
Fig. S17. Physical posteriors.
Fig. S18. The May 2019 transit.
Table S1. Kepler-only fits.
Table S2. Transmission spectrum.
Table S3. Transit timings.
References (42–72)
Additional Files
Supplementary Materials
This PDF file includes:
- Supplementary Materials and Methods
- Fig. S1. The “Phantom” star.
- Fig. S2. Kepler detrending.
- Fig. S3. Kepler detrending comparison.
- Fig. S4. HST image rotation.
- Fig. S5. HST hook model comparison.
- Fig. S6. HST centroids.
- Fig. S7. Spectral analysis.
- Fig. S8. Transmission spectrum.
- Fig. S9. Wavelength solution.
- Fig. S10. Wavelength-dependent pixel sensitivity.
- Fig. S11. Modeling the uncataloged source contamination.
- Fig. S12. Transit timing variations.
- Fig. S13. Residual analysis.
- Fig. S14. Chromatic test.
- Fig. S15. Mass constraints.
- Fig. S16. Model posteriors.
- Fig. S17. Physical posteriors.
- Fig. S18. The May 2019 transit.
- Table S1. Kepler-only fits.
- Table S2. Transmission spectrum.
- Table S3. Transit timings.
- References (42–72)
Files in this Data Supplement:
